A futuristic entrepreneur wants to start a cruise line company and needs to build a cruise ship that will not only float on a gas giant, but be habitable throughout a 7 day trip (for the uber-rich of course).

What sort of ship would need to be built to survive a week on a gas giant?

Ideally, the ship would float on its own, due to buoyant forces.

In regards to the level of technology required: it should be as advanced as it needs to be in order to accomplish this goal - i.e. hand-wavey technology is allowed if there are no other options.

$\begingroup$What is the difference between a boat and a balloon? Because you can float a balloon on Earth in the atmosphere, a boat in the ocean. Given the composition of a gas giant, a balloon might be more applicable.$\endgroup$
– kingledionJan 11 '18 at 19:51

$\begingroup$If you gas giant is like Jupiter, you can't make it significantly buoyant based on the type of gas as hydrogen/helium is the primary atmosphere the lightest possible gases. So you need to use hot hydrogen/helium as your lifting gas. A detailed answer will need to know the temperature and pressure to calcuate buoyant force and materials requirements unless everything is just hand-wavium.$\endgroup$
– Gary WalkerJan 11 '18 at 20:25

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$\begingroup$You shouldn't accept an answer so soon. Give it at least 24 hours, the person with the best answer might be asleep right now!$\endgroup$
– kingledionJan 11 '18 at 21:58

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$\begingroup$@AustinA I updated with more info on other gas giants$\endgroup$
– kingledionJan 12 '18 at 9:47

7 Answers
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Analyzing Jupiter

First off, since Jupiter doesn't have a surface, the 1 bar pressure altitude is commonly referred to as the surface. Surface temp (from a NASA fact sheet) is, in that case, around 165 K; cold but not cold enough that you couldn't insulate it trivially. So in this region, pressure and temperature are not a major concern. At this altitude and nearby you will get clouds of ammonium hydrosulfide, with water clouds also in denser areas below. These aren't really a problem, either.

Instead, what you need to worry about is the 100 m/s winds at this altitude. The wind speeds do vary by zone, so there are areas between bands where wind speed is near zero. A graph of wind speed by latitude illustrates this.

These wind speeds are in the jets, in the 0.7-1 bar region all the way down to at least 22 bar, which is as far as the Galileo probe got to check on them.

So a better solution might be to fly higher, above the clouds. At about the 0.1 bar zone (or 10$^4$ Pa on the top chart; 50 km altitude above the 1 bar level), the winds have mostly decayed away (they decay away in 3 scale heights, and a scale height is 27 km on Jupiter), and force on a craft from wind will be reduced by a factor of 10. Temperature is even lower at about 112 K, but with low air pressure and little wind, there won't be too much heat loss. Insulation should again be trivial.

So now we can handle pressure, temperature, and winds at this altitude, all that remains is to deal with the gravity. With low air pressure, floating will then be hard. In fact, it will be close to impossible. The atmosphere of Jupiter is primarily Hydrogen and Helium in the first place, meaning that hydrogen balloons won't float like they do on Earth. Even if you kept your balloon's gas filled envelope at a very high temperature, the density difference would be only marginal with the surrounding air. You could lower the balloon's envelop pressure to drop density further, but then you would need a rigid envelope, further increasing your required structural mass and making the balloon less efficient still.

More rigorously, the density of Jupiter's atmosphere at an altitude of 1 bar is 0.16 kg/m$^3$. If we can hold our balloon envelope at vaccuum, then we can lift 32 tons of mass per Hindenburg of volume. Unfortunately, that isn't really that much; the Hindenburg itself was more like 230 tons of mass. At 1 bar of pressure, the forces on an envelope held at vacuum will be tremendous, not to mention the shear forces from 100 m/s winds.

Finally, the biggest problem with your cruise ship idea is that your passengers will be crushed by the gravity. With gravity around 25 m/s$^2$, it will be much higher than on Earth. Not only will that make already-nearly-impossible floating even harder, it will probably kill all your passengers.

Other Gas giants

Saturn's atmosphere is similar to Jupiter's. In fact, the density at the 1 bar level is slightly higher (0.19 kg/m$^3$), despite its lower surface gravity (1.06$g$). On the other hand, its scale height is larger (52 km) and wind speeds are much higher, up to 400 m/s at the equator. Also, as you can see in its graph, its 'surface' is the 0.1 bar level, not 1 bar. This means that you will see the very high wind speeds at that lower pressure level. Thus, even floating at high altitudes with nearly zero lift, you still get buffeted by extremely strong winds.

Assuming you can survive the high winds at the 0.1 bar level, given the density of the atmosphere, a spherical balloon envelope 1 km in diameter will have a volume of about 0.5 km$^3$ and a lift of 9500 tons; enough for a tourist vessel. A full on modern cruise ship of 100,000 tons would require a spherical balloon of a little over 2 km diameter.

The other gas giants are considerably more iffy regarding data; Jupiter and Saturn have had the attention of Galileo and Cassini, respectively, for many years. Uranus and Neptune have not. NASA's Uranus fact sheet gives a very promising atmospheric density of 0.42 kg/m$^3$. However, wind speeds are not well known and could be up to 250 m/s. If there are lower winds speeds at this altitude, then this would decrease the volume of vacuum needed by a factor of 2. However, this really only reduces the speed at which you must wave your hands to make this a reality.

Conclusion: Wave many hands

On a gas giant with Jupiter's gravity, the only way to save your passengers is with some magical gravity canceling device. I would assume that having such a device would then make floating your ship trivial. But without hand-wavey solutions, not only can you not float in Jupiter's atmosphere, you will kill your human passengers trying to do so.

Other gas giants are less magic-requiring, in that surface gravity will be close enough to Earth's to not kill your passengers. However, the problems with floating in an atmosphere that is already made of helium, the least dense element, remain. Even at vacuum, you have almost no lift. The solution is materials of indeterminately high strength, in order to hold a (very, very) large envelope at vacuum against atmospheric pressure, while not disintegrating in the high winds. Just to be clear, given the forces involved in holding a cubic kilometer or so at vacuum against 1 bar pressure, this is nearly as hand-wavey as a gravity canceling device.

In fact, the larger the better. If you want to ensure the passenger's comfort, you will need the most mass and inertia in your balloon as possible to keep the winds from buffeting them uncomfortably. That means, you will need a vacuum chamber kilometers across; like a mini-moon floating in a Saturnian sky.

$\begingroup$2.5 g would not kill any healthy person. It would be uncomfortable, but tolerable.$\endgroup$
– vszJan 12 '18 at 5:29

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$\begingroup$@vsz Fundamentally false. How much do you weigh? Multiply that by 1.5 and put that weight on your back. Tell me how long you will function. When I rowed college varsity crew, I could max squat about 2.5 times my body weight...that is how much I would weigh on Jupiter. If a 22 year old college athlete couldn't stand up, the tourists are screwed.$\endgroup$
– kingledionJan 12 '18 at 8:56

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$\begingroup$@kingledion : I personally hit 3.5 g when flying gliders, and not only survived, but was fully functional and in control. People can endure 3 g without passing out, long-term. Racecars, roller coasters etc. can have even higher accelerations (and I wasn't talking about 8-9 g in fighter planes, because that requires special training and equipment). en.wikipedia.org/wiki/G-force#Typical_examples$\endgroup$
– vszJan 12 '18 at 9:09

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$\begingroup$@kingledion : indeed, for months or years, even 1.5 g would be dangerously unhealthy. For a few hours, 2.5 g should be tolerable, even if uncomfortable. Or, better yet, you could submerge them in water, then it won't be such a big problem to move around. You don't even have to submerge them fully. Up to chest or neck, so they can comfortably walk around. (by the way, some roller coasters can go up to 6g)$\endgroup$
– vszJan 12 '18 at 11:09

In other words, if you want to float close to the surface, you're in a cold, gaseous region with a low density. This isn't great; according to Archimedes' principle, any lifting gas you use must be less dense than the medium surrounding it. The atmosphere outside is already not too dense, which is problematic.

1. Float low

High in Jupiter's atmosphere, there's a smooth transition to the interplanetary medium, where you see a lot more hydrogen. Lower, near (and below) $P=1\text{ bar}$, $\mu$ is higher and $\rho$ is also higher. This means that your lifting gas doesn't have to be as lightweight as if you were trying to float near the top of the atmosphere.

As kingledion's chart shows, temperature is roughly constant from $P=10^{3}\text{ bars}$ to $P=10^0\text{ bars}$ - i.e. right below the "surface" of Jupiter. However, at the surface, it rapidly increases, as density and pressure rapidly decrease. I would aim for this region - at the surface or a bit below it. You'll probably be stuck in the same temperature range, $150\text{ K}$ to $200\text{ K}$, and pressure is the main difference.

2. Don't go for a vacuum airship.

We already know that that sort of thing is hard on Earth. In the regions we're considering, the outside pressure is going to be even stronger. Sure, you can maybe mitigate that with whatever tech you've developed by the time humans can get to Jupiter, but you can only handwave away so much. It just won't work at this part of Jupiter.

Instead, use something like heated hydrogen! This is why I like the low-temperature region of the planet. The surrounding gas will have a higher density and a lower temperature, and so any particular lifting gas at a certain temperature will be more effective. Obviously, hydrogen is flammable, but hey, it's cheaper than helium, and if you're safe, maybe things won't go so poorly.

Let's say the ship is designed like a Zeppelin, with a chamber of gas of volume $V_g$ and a cabin of volume $V_c$. The mass of the gas is $m_g$ and the mass of the cabin is $m_c$. We then need, for the ship to float at equilibrium,
$$F_{\text{buoyant}}=(m_g+m_c)g=\rho_J(V_g+V_c)g=F_{\text{gravity}}$$
where $\rho_J$ is again the atmospheric density of Jupiter at $P=1\text{ bar}$, and $g$ is Jupiter's surface gravity. Now, $m_g=\rho_gV_g$, where $\rho_g$ is the density of the gas. Therefore,
$$(\rho_gV_g+m_c)g=\rho_J(V_g+V_c)g$$
Rearranging, cancelling and solving for $\rho_g$, we find
$$\rho_g=\rho_J\left(1+\frac{V_c}{V_g}\right)-\frac{m_c}{V_g}$$
Given that $V_c\ll V_g$, we can appxoximate this as
$$\rho_g\approx\rho_J-\frac{m_c}{V_g}$$
Choose your cabin mas wisely, and adjust the other two parameters as you desire. For the Hindenburg, for instance, $V_g\approx200,000\text{ m}^3$. This actually allows us to have a comfortable cabin mass, if we're willing to raise the temperature enough inside. You'd be able to look for something in the vicinity of a couple tens of tons. Not a lot, but enough.

Let's use the ideal gas law for the inside of the gas sac. Assume $p=1\text{ bar}$ (roughly) and $\rho_g\approx0.10\text{ kg m}^{-3}$. Then we have
$$P=\rho_g \frac{k_b}{\mu_gm_u}T_g$$
where $k_B$ is the Boltzmann constant, $\mu_g\approx1$ is the mean molecular weight of the gas, and $m_u$ is one atomic mass unit. I find that $T_g\approx121\text{ K}$. We can afford to have a higher $\rho_g$, too, so the hydrogen gas can be a bit hotter. Now, this means we must have a smaller cabin mass, but still.

3. Insulate well

It's all very well and good having a warm bubble in a cold atmosphere, but if there's heat transfer, your ship will soon freeze. I've continued to do reading on possible materials without much luck (although I daresay that someone else probably knows enough to find something good), but then again, I'm not great at materials science.

I do think that you'll want to have some sort of composite skin on your airship. You need it to be able to survive pressures both a bit higher and lower than on Earth - while still keeping the hydrogen gas inside - as well as withstanding some pretty cold conditions. Neither of these are overly problematic; there are plenty of materials that can do this.

The problem is, quite simple, one of weight. Anything that flies - and this ship will fly, in a sense - needs to take weight into account. I've already done this when considering the mass of the crew cabin. However, I'm a lot more concerned about covering the envelope with something that's strong, lightweight, and a good thermal insulator.

$\begingroup$A super-material allowing a vacuum airship is a whole lot more likely than the antigravity that a different answer calls for.$\endgroup$
– SpencerJan 11 '18 at 23:49

$\begingroup$You say Hydrogen is flammable, but this is only a concern if Oxygen is available, which it isn't.$\endgroup$
– DharaJan 12 '18 at 13:13

$\begingroup$@Dhara I had been thinking of the oxygen in the crew cabin; presumably, they would need a large supply to breathe, and if there are oxygen tanks anywhere near the gas sac - and there almost certainly would be - you could have a problem. If you had a spark, like on Apollo 13, the effects could be a lot worse.$\endgroup$
– HDE 226868♦Jan 12 '18 at 14:34

Although we could make a balloon, or even a vast construct like Buckmaster Fuller's "Cloud 9", one issue which you haven't though of is how are you going to board and disembark?

Cloud Nine (tensegrity sphere). For Earthly flight, you would need a sphere almost a kilometre in diameter as a minimum

You will be blasting off through the atmosphere of a gas giant, and need some pretty incredible rocket power to overcome the gravity as well. In essence, you would need a spaceship to enter the atmosphere, deploy a balloon for a week, then blast off (probably through the balloon) to escape. This is the sort of model proposed by the British Interplanetary Society when they worked on their "Project Daedalus" interstellar probe, with harvesters in the atmosphere of Jupiter gathering 3He for the fusion reactor.

Daedalus in orbit

Instead of the harvester under the balloon, you have the spaceship

For people aboard, it will be rather uncomfortable, since the spacecraft will need to mass as little as possible, yet still require massive radiation shielding, making the interior cramped. As well, a nuclear reactor or fusion reactor will need to be running constantly to deliver heat energy to the balloon envelope, and the ship will probably also be running a compressor and liquifier in order to build up a supply of reaction mass to blast back into orbit (in this case, you need thrust more than ISP). So there will be lots of background noise, in addition to any noises the balloons cables are making in the high winds.

So while it certainly will be an adventure cruise, it will be the sort of adventure cruise only very dedicated people will be willing to take.

Could a ship be made to survive a week inside Jupiter's atmosphere? Certainly.

There is nothing particularly terrible there, hydrogen and helium starting sparse and cold and getting denser and warmer as you go in, no problem for a controlled entry and decent. You can be nearly 1000km in before you get to Earth pressures or temperatures and reach some clouds of other gases. It would be technically challenging to be buoyant in mostly hydrogen, but perhaps a rigid vacuum chamber could be handwaved light enough.

There are big storms there, thousands of km across (not counting the stable one bigger than earth) and 100km tall, which can move hundreds of km per hour, but they seem to mostly stay in belts so could be avoided.

Could humans be happy during that week? Less so.

The gravity in clouds is about 2.5 times that of Earth. That is known to be survivable, but it would be a hassle.

Many other answers have already covered the dangers associated with Jupiter-like Gas Giants. In this answer I'll endeavour to suggest a few things that might make engineering the existence of these flights more viable.

Engineer your Gas Giant Differently: Most Gas Giants are made mostly of Helium and Hydrogen. This is a problem, as other answers have discussed, because they are the two lightest chemical elements known to man. However, if you had an unusual or constructed Gas Giant made mostly of Xenon and Neon for example, lifting gasses would be far more effective.

Engineer Your Cruise Vehicle Differently: Buoyancy may not be powerful enough to keep "afloat" in most Gas Giants but other methods of aeronautics also still work. Lifting bodies like wings are viable, if less effective, in these environments. Also possible in this environment are jets and propellers. They are also less effective due to the dense atmosphere but this can be mitigated with speculative engineering (not speculative science). If you make your intakes very large and have the technology for the few particles going thorough your engine to exit at a very high speed then that will offset the lack of atmosphere. Also, since the atmosphere of Jupiter is contains a number of Hydrocarbons and even Space Shuttle Fuel (Hydrazine), it may be possible to get the air flowing through the engine to a high enough temperature and pressure to ignite them. By combining all three of these ideas you can imagine a huge B2 Bomber shaped thing with large ducted jets built flush into the fuselage. If you fill most of the wings with low pressure Hydrogen/Helium and build your radiators inside the wings so that the waste heat from your ship heats up the lifting gas, you may well be on to a winner.